A single defocused star image contains sufficient information to uniquely determine the spatial phase fluctuations
of the incident wavefront. A sensor which responds to the intensity distribution in the image produces signals
proportional to the wavefront curvature within the pupil and the radial slope at the pupil boundary. Unlike Roddier's
differential curvature sensing technique, a single-image sensor does not cancel intensity fluctuations due to atmospheric
scintillation. However, it has been shown that at typical astronomical sites the scintillation signal is negligibly small.
A single-image curvature sensor can theoretically achieve a signal-to-noise ratio of order Q approximately equals r20/(lambda) z0
where r0 is Fried's correlation length, (lambda) is the wavelength, and z0 is the root-mean-square distance through
the atmosphere, weighted by the refractive index structure constant C2n. This is more than adequate for AO systems
whenever D/r0 <EQ Q6/5. Such a sensor can be very simple, optically and mechanically, and has lower detector read
noise than a comparable differential system. The concept has been tested in the laboratory by introducing, and
detecting, spherical aberration in a simple optical system.
Copyright 1994 Society of Photo-Optical Instrumentation Engineers.
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